In each of these questions, two equations (I) and (II) are given . You have to solve both the equations and give answer
I. ` (9)/( sqrt( x)) + (19)/( sqrt(x)) = sqrt( x) `
II. ` y^(5) - (( 2 xx 14) ^((11)/(2)))/( sqrt(y) ) = 0 `

Options

A. If ` x gt y `
B. If ` x lt y `
C. If ` x ge Y`
D. if x = y or relationship between x and y cannot be established

Answer

To solve the given equations step by step, we will start with Equation I and then move on to Equation II.

### Step 1: Solve Equation I
The first equation is:

\[ \frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x} \]

**Combine the fractions on the left-hand side:**

\[ \frac{9 + 19}{\sqrt{x}} = \sqrt{x} \]

This simplifies to:

\[ \frac{28}{\sqrt{x}} = \sqrt{x} \]

**Multiply both sides by \(\sqrt{x}\) to eliminate the fraction:**

\[ 28 = x \]

Thus, we find:

\[ x = 28 \]

### Step 2: Solve Equation II
The second equation is:

\[ y^5 - \frac{(2 \times 14)^{\frac{11}{2}}}{\sqrt{y}} = 0 \]

**First, calculate \(2 \times 14\):**

\[ 2 \times 14 = 28 \]

So the equation becomes:

\[ y^5 - \frac{28^{\frac{11}{2}}}{\sqrt{y}} = 0 \]

**Multiply through by \(\sqrt{y}\) to eliminate the fraction:**

\[ y^5 \cdot \sqrt{y} - 28^{\frac{11}{2}} = 0 \]

**This can be rewritten as:**

\[ y^{5 + \frac{1}{2}} = 28^{\frac{11}{2}} \]

**Combine the exponents:**

\[ y^{\frac{11}{2}} = 28^{\frac{11}{2}} \]

**Taking the \(\frac{2}{11}\) power of both sides:**

\[ y = 28 \]

### Step 3: Compare \(x\) and \(y\)
From the above calculations, we have:

\[ x = 28 \quad \text{and} \quad y = 28 \]

Thus, we find:

\[ x = y \]

### Final Answer
The relationship between \(x\) and \(y\) is:

\[ x = y \]